1、Designation: E 2262 03Standard Practice forEstimating Thurstonian Discriminal Distances1This standard is issued under the fixed designation E 2262; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number
2、 in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice describes procedures to estimate Thursto-nian discriminal distances (that is, d values) from dataobtained on two samples. Proc
3、edures are presented for fourforced-choice methods (that is, the triangle, the duo-trio, the3-alternative-forced-choice (or 3-AFC) and the 2-AFC (alsocalled the directional difference test), theA/Not-Amethod, theSame-Different method and for data obtained from orderedcategory scales. Procedures for
4、estimating the variance of dare also presented. Thus, confidence intervals and statisticaltests can be calculated for d.1.2 The procedures in this document pertain only to theunidimensional, equal-variance model. Other, more compli-cated Thurstonian models, involving multiple dimensions andunequal v
5、ariances exist but are not addressed in this standard.The procedure for forced-choice methods is limited to dichoto-mous responses. The procedure for the A/Not-A methodassumes equal sample sizes for the two samples. The procedurefor the Same-Different method assumes equal sample sizes forthe matched
6、 and unmatched pairs of samples. For all methods,only unreplicated tests are considered. (Tests in which eachassessor performs multiple (that is, replicated) evaluationsrequire different analyses.)1.3 Thurstonian scaling is a method for measuring theperceptual difference between two samples based on
7、 a proba-bilistic model for categorical choice decision making. Themagnitude of the perceived difference, d, can be estimatedfrom the assessors categorical choices using the methodsdescribed in this practice (SeeAppendix X3 for a more detaileddescription of Thurstonian scaling).1.4 In theory, the Th
8、urstonian d does not depend on themethod used to measure the difference between two samples.As such, d provides a common scale of measure for comparingsamples measured under a variety of test conditions. Forexample, Thurstonian scaling can be used to compare productsmeasured under different test con
9、ditions, to compare panels(trained, consumer or both) that have evaluated the samesamples (using the same or different test methods) and tocompare test methods on their ability to discriminate samplesthat exhibit a fixed sensory difference.1.5 This standard may involve hazardous materials, opera-tio
10、ns and equipment. This standard does not purport to addressall of the safety concerns, if any, associated with its use. It isthe responsibility of the user of this standard to establishappropriate safety and health practices and determine theapplicability of regulatory limitations prior to use.2. Re
11、ferenced Documents2.1 ASTM Standards:E 253 Terminology Relating to Sensory Evaluation of Ma-terials and Products2E 456 Terminology for Relating to Quality and Statistics2E 460 Practice for Determining Effect of Packaging onFood and Beverage Products During Storage2E 679 Practice for Determination of
12、 Odor and Taste Thresh-olds By a Forced-Choice Ascending Concentration SeriesMethod of Limits2E 1432 Practice for Defining and Calculating Individual andGroup Sensory Thresholds from Forced-Choice Data Setsof Intermediate Size2E 1593 Practice for Assessing the Efficacy of Air FreshenerProducts in Re
13、ducing Sensorialy Perceived Indoor AirMalodor Intensity2E 1627 Practice for Sensory Evaluation of Edible Oils andFats2E 1697 Test Method for Unipolar Magnitude Estimation ofSensory Attributes2E 1810 Practice for Evaluating Effects of Contaminants onOdor and Taste of Exposed Fish2E 1879 Guide for Sen
14、sory Evaluation of Beverages Con-taining Alcohol2E 1885 Test Method for Sensory Analysis-Triangle Test2E 1958 Guide for Sensory Claim Substantiation2E 2049 Guide for Quantitative Evaluation of Fragrance/Odors for Shampoos and Hair Conditioners2E 2164 Test Method Directional Difference Test22.2 ASTM
15、Publication:Manual 26 Sensory Testing Methods, 2nd Edition21This practice is under the jurisdiction of ASTM Committee E18 on SensoryEvaluation of Materials and Products and is the direct responsibility of Subcom-mittee E18.03 on Sensory Theory and Statistics.Current edition approved July 10, 2003. P
16、ublished Aug. 2003.2Annual Book of ASTM Standards, Vol 15.08.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.2.3 ISO Standard:ISO 5495 Sensory AnalysisMethodologyPaired Com-parison33. Terminology3.1 For definitions of terms relating
17、to sensory analysis, seeTerminology E 253, and for terms relating to statistics, seeTerminology E 456.3.2 Definitions of Terms Specific to This Standard:3.2.1 dthe Thurstonian discriminal distance is the dis-tance between the means of the distributions of sensorymagnitudes of the two samples in the
18、test (see Appendix X3).3.2.2 dthe statistic used to estimate d based on the dataobtained from the test.3.2.3 choice proportion (Pc)the expected proportion ofresponses from a forced-choice method (for example, if there isno perceptible difference between the samples in a triangle test,Pc= 1/3. If the
19、re is a perceptible difference, Pc 1/3).3.2.4 observed choice proportion (pc)the statistic used toestimate choice proportion, Pc, where pc= x/n, where x is theobserved number of correct responses and n is the sample size.4. Summary of Practice4.1 Determine the type of data collected on the two sampl
20、es:data from a forced-choice test, an A/Not A test, a same-different test or an ordered category scale.4.2 For forced-choice tests, reference the table that corre-sponds to the test method (that is, triangle testTables X1.1and X1.2; duo-trio testTables X1.3 and X1.4; 3-AFC testTables X1.5 and X1.6;
21、or 2-AFC testTables X1.7 and X1.8).Identify the entry in the table closest to the observed choiceproportion (pc) from the test. Read the estimated value of d(that is, d) from the corresponding row and column headingsof the table. Estimate the variance of d by referencing theappropriate table for the
22、 test method. Find the value of B thatcorresponds to the value of d obtained in the first step.4Theestimated variance of disS2(d) = B/n, where n is the samplesize. Use the estimates d and S2(d) to construct confidenceintervals and tests of hypotheses related to the objectives of theresearch.4.3 For
23、the A/Not A method, tally the observed choiceproportions of “A” responses for the A sample and the “A”responses for the Not-A sample. Read the value of d fromTable X1.9 in the column that corresponds to the observedchoice proportion of the “A” responses for the Not-A sample(pna) and the row that cor
24、responds to the observed choiceproportion of the “A” responses for the A sample (pa). Thesame method is used to estimate the variance of d, S2(d),using Table X1.10.4.4 For the Same-Different method, tally the proportion of“same” responses for the matched pairs of samples (that is,A/A or B/B) and the
25、 proportion of “same” responses for theunmatched pairs of samples (that is, A/B or B/A). Read thevalue of d from Table X1.11 in the column that corresponds tothe observed proportion of “same” responses for the un-matched pairs (ps/u) and the row that corresponds to theobserved proportion of the “sam
26、e” responses for the matchedpairs (ps/m). The same method is used to estimate the varianceof d, S2(d), using Table X1.12.4.5 For ordered category scales, a rapid, table-look-upapproach is used. For each sample, the category scale data arecollapsed into two categories. One sample is selected to be th
27、e“A” sample and the other sample is selected to be the “Not-A”sample. Choice proportions are tallied for each sample and thevalues of d and its variance, S2(d), are obtained from TablesX1.9 and X1.10, respectively, by the same techniques used inthe A/Not A method.5. Significance and Use5.1 Under the
28、 assumptions of the model, the Thurstonianmodel approach to measuring the perceived difference betweentwo samples (whether overall or for a specific attribute) isindependent of the sensory method used to collect the data.Converting results obtained from different test methods to dvalues permits the
29、assessment of relative differences amongsamples without requiring that the samples be compared toeach other directly or that the same test methods be used for allpairs of samples.5.2 Thurstonian scaling has been applied to:5.2.1 Creating a historical database to track differencesbetween production a
30、nd reference samples over periods inwhich different test methods were used to measure the differ-ence,5.2.2 Comparing the relative sensitivities of different usergroups and consumer segments,5.2.3 Comparing trained panels that use different measuringtechniques,5.2.4 Comparing the relative sensitivit
31、ies of consumersversus trained panels,5.2.5 Comparing different methods of consumer testing (forexample, CLT versus HUT, preference versus hedonic scales,etc.), and5.2.6 Comparing different discrimination test methods.6. Procedure6.1 Forced-Choice MethodsThe relationship between dand the expected ch
32、oice proportion, Pc, is different for differentforced-choice methods because the decision rule used by theassessors varies from one method to another (see AppendixX3). As a result, different tables are required to estimate ddepending on the method used. Tables for the four mostcommonly used methods
33、are presented. The estimated value ofd (that is, d) is obtained as follows:6.1.1 Compute the observed choice proportion as pc= x/n,where x is the observed number of correct responses and n isthe sample size.6.1.2 Obtain d by entering the table in Appendix X1 thatcorresponds to the test method used:
34、triangle test (Table X1.1),duo-trio (Table X1.3), 3-AFC (Table X1.5) or 2-AFC (TableX1.7). Find the entry in the table that is closest to the observed3Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036.4The variance of d is a complicated functio
35、n of the true value of d and thedecision rule whenassociated with the test method being used (see Appendix X3).However, regardless of the test method, the variance of d can always be expressedas S2(d)=B/n, where the parameter B captures all of the information concerning thetest method, and n is the
36、sample size. The values of B have been tabulated to makethe calculation of the variance of d a simple task.E2262032value of pc. The value of d, accurate to one decimal place, isthe row-label of the table corresponding to the selected entry.The second decimal place of d is the column-label of the tab
37、lecorresponding to the selected entry.6.1.3 Obtain the estimated variance of d as follows. Enterthe appropriate table in Appendix X1: triangle test (TableX1.2), duo-trio (Table X1.4), 3-AFC (Table X1.6) or 2-AFC(Table X1.8). Find the value of B in the row and column thatcorrespond to the value of d
38、obtained in 6.1.2. Compute theestimated variance of dasS2(d) = B/n, where n is the samplesize. Use the estimates d and S2(d) to construct confidenceintervals and tests of hypotheses related to the objectives of theresearch.6.2 A/Not A MethodCompute the choice proportions ofthe two samples, pa= xa/n
39、and pna= xna/n, where xais thenumber of times the “A” sample is chosen as being “A,”, xnaisthe number of times the “Not-A” sample is chosen as being“A” and n is the sample size.NOTE 1This practice only considers the case where the number of“A” samples equals the number of “Not-A” samples, n = na= nn
40、a.6.2.1 Read the value of d from Table X1.9 in Appendix X1in the column that corresponds to the observed choice propor-tion of the “Not-A” sample (pna) and the row that correspondsto the observed choice proportion of the “A” sample (pa).6.2.2 To obtain an estimate of the variance of d, read thevalue
41、 of B from Table X1.10 in Appendix X1 using the sametechnique as in 6.2.1. The variance estimate is S2(d) = B/n,where n is the sample size.6.3 Same-Different MethodCompute the choice propor-tions for the matched (m) and unmatched (u) pairs of samples,ps/m= xs/m/n and ps/u= xs/u/n, where xs/mis the n
42、umber of“same” responses for the matched pairs (A/A or B/B) evalu-ated, xs/uis the number of “same” responses for the unmatchedpair and n is the number of matched or unmatched pairsevaluated.NOTE 2This practice only considers the case where the number ofmatched pairs equals the number of unmatched p
43、airs, n = nm= nu.6.3.1 Read the value of d from Table X1.11 in AppendixX1 in the column that corresponds to the observed proportionof “same” responses for unmatched pair (ps/u) and the row thatcorresponds to the observed proportion of “same” responsesfor the matched pair (ps/m).6.3.2 To obtain an es
44、timate of the variance of d, read thevalue of B from Table X1.12 in Appendix X1 using the sametechnique as in 6.3.1. The variance estimate is S2(d) = B/n,where n is the sample size.6.4 Ordered Category ScalesA rapid, table-look-upmethod is described. The method collapses the category-scaledata into
45、two categories, regardless of the number of categorieson the physical scale used to collect the data. It is recognizedthat information detail is lost by collapsing the data into twocategories. However, the estimates of d and its variance,S2(d), obtained from the technique are accurate. The compu-tat
46、ional ease offsets the small loss of accuracy incurred.6.4.1 Tally the frequency distributions of category scaleratings for the two samples. Select the sample with the lowermedian rating to be the Not-A sample. Select the sample withthe higher median rating to be the A sample.6.4.2 Collapse the freq
47、uency data for each sample into twocategories as follows. Identify the category in which themedian of the Not-A sample occurs. Pool the number ofresponses from that category and all lower categories for eachsample separately and record the totals in the 2-by-2 tableunder “Low” (that is, the ynaand y
48、atallies, below). Pool thenumber of responses for the remaining, higher categories foreach sample separately and record the totals in the 2-by-2 tableunder “High” (that is, the xnaand xatallies, below).Sample Low HighNot-A ynaxnaA yaxa6.4.3 Compute the choice proportions of the two samples,pa= xa/n
49、and pna= xna/n, where xaand xnaare obtained fromthe table above and n is the sample size, common to bothsamples.6.4.4 Apply the same technique used in theA/NotAmethod(see 6.2). Read the value of d fromTable X1.9 inAppendix X1in the column that corresponds to the observed choice propor-tion of the Not-A sample (pna) and the row that corresponds tothe observed choice proportion of the A sample (pa).6.4.5 To obtain an estimate of the variance of d, read thevalue of B from Table X1.10 in Appendix X1 using the sametechnique as in 6.
